Botlek Railway Tunnel: Comparison between BorTas, LDesign and analytical solutions

Transcription

1 Botlek Railway Tunnel: Comparison between BorTas, and analytical solutions Ir. C.B.M. Blom, Delft, 2001 Holland Railconsult, Delft University of Technology CONCEPT!! Wednesday, September 26,

2 1 References [1] Validatieberekeningen ANSYS-model, GP-SJL [2] Nieuwe validatie 1 en 2.xls [3] Lining behaviour - solutions of coupled segmented rings in soil, Preliminary Thesis Design Philosophy of Concrete Linings of Shield Driven Tunnels in soft soils, Chapter 3, Delft University of Technology , September 2001, C.B.M. Blom 2 Introduction load cases Loading in BorTas has been defined as loading at the outer circumference of the lining. Loading in analytical solution and has been defined as loading at system radius. To compare calculation results both loading has to be equal. System radius: 4525mm Lining thickness: 400mm Acting radius for loading in BorTas: =4725mm Acting radius for loading in analytical solutions and : 4525mm Multiplication factor loading from BorTas to solutions and : In all cases occurs ground support with E g =4000Mpa Concrete Young s modulus: E b = 33500MPa Single ring, 7 segments and keystone. Keystone position = -12 In analytical solution and, the key stone is not considered. s top [MPa] *1.044 s flank [MPa] *1.044 BorTas Others BorTas Others Validation 1.1 uniform loading Validation 1.2 Ovalisation loading stiff rotation in longitudinal joints, K 0 =0.9 Validation 1.3 Ovalisation loading rotation stiffness in longitudinal joints by Janssen, K 0 = 0.9 Validation 2.0 Ovalisation loading rotation stiffness in longitudinal joints by Janssen -a = 1.1 K 0 = b = 1.3 K 0 = c K 0 = d K 0 = e K 0 = f K 0 =

3 3 Validation 1.1 Uniform loads u_rad [mm] Validatie phi [gr] Bortas Comparing BorTas deformation due to pure compression has non uniform deformed shape. Results of analytical solution and agree well. 4 Validation 1.2 Ovalisation and stiff longitudinal joints In BorTas rotation stiffness values in longitudinal joints have been increased, so a homogeneous ring has to be approached. and calculations will assume the homogeneous ring. Presented results are excluding compression to purely compare deformations due to ovalisations. Validation 1.2 u_rad [mm] Analutical phi [gr] Bortas 1.2 It shows that deformations by BorTas validation 1.2 are not equal to a homogeneous ring. and approach agree well. 3-8

4 5 Validation 1.3: Ovalisation and normal stiffness longitudinal joints Validation Bortas 1.3 In validation 1.3 BorTas is mostly functioning without any adaptations made for the academic cases. It shows that results from all approaches agree well. solutions does agree very well because all longitudinal joints behave within the non-reduced branch of M-Phi relation for the concrete joints. 6 Validation 2: Increasing ovalisation Validation 2a and 2b are equal to validation 1.1 and 1.3. Both results have already been presented a: k 0 =1 see validation b: k 0 =0.9 see validation

5 6.3 2-c: k 0 =0.8 Validation 2c: k= Bortas The three models agree very well. Non linearity occurs for longitudinal joint behaviour. Still analytical approach gives very suitable agreement. 5-8

6 6.4 2-d: k 0 =0.7 Validation 2-d k= BorTas BorTas and agree very well. The analytical approach is going to give discrepancies due to made basic assumptions in this model (see [3]). Large Non linear longitudinal joint behaviour is the reason for discrepancies. Still values do confirm e: k 0 =0.6 Validation 2-e: k= BoTtas

7 Again BorTas and agree very well. Discrepancies with analytical solution do increase by more non linear longitudinal joint behaviour f: k 0 =0.5 Validation 2-f: k= BoTtas -6-8 Again BorTas and agree very well. Discrepancies with analytical solution do increase by more non linear longitudinal joint behaviour. 7-8

8 7 Conclusions Uniform loading must result in uniform compression. Both analytical solutions and satisfy this result. BorTas has an unexpected field of deformations. According to the designer this can be explained by influence of the third dimension involving axial jack forces and wedge shape of the key segment. The given cases confirm behaviour of BorTas in analytical solutions and for ovalisation loading. When longitudinal joint behaviour is near linear behaviour even analytical solutions well agree solutions of more sophisticated approaches in and BorTas. Until very large non linear behaviour in longitudinal joints and BorTas give suitable results. In rotation stiffness by Janssen has implemented. In BorTas the rotation stiffness has been arranged by contact elements. Using analytical approach for rotation stiffness in the analytical solution also give suitable results if degree of non linear behaviour is not too high. Comparing the models it is concluded that longitudinal behaviour in BorTas has been modelled by mean of theory. Remark: One has to remind that these cases are academic cases. Involved ground stiffness is very low, almost not present. Still at time of great deformation ground support is of significant influence (case 2-f: =68% of active loading has given back to ground) 8-8